相关论文: Pricing rule based on non-arbitrage arguments for …

Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following It\^o-Mckean skew Brownian motion. While the Corns-Satchell market model is…

We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and…

We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…

We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…

There is a well developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying…

We prove that if the Black-Scholes formula holds with the spot volatility for call options with all strikes, then the volatility parameter is constant. The proof relies some result on semimartingales (Theorem 2) of independent interest.

Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…

We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale…

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage…

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an…

This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a…

In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A…

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…

We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market…

We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical…